May 7 14:48
4 mos ago
24 viewers *
Spanish term
haces de circunferencias
Spanish to English
Other
Mathematics & Statistics
Hola
estoy traduciendo una asignatura de Ingería Civil que se llama "Geometría métrica y descriptiva". Dentro de la asignatura se tratan diversos temas, entre ellos "Haces de circunferencias".
Contexto:
Haz de circunferencias
Haz de circunferencias, son todas las circunferencias que comparten un mismo eje radical.
Para que esto ocurra todas tendrán sus centros sobre la misma recta diametral y que pasen por los dos mismos puntos del eje radical.
Al eje radical común se le llama base del haz.
Gracias de antemano.
estoy traduciendo una asignatura de Ingería Civil que se llama "Geometría métrica y descriptiva". Dentro de la asignatura se tratan diversos temas, entre ellos "Haces de circunferencias".
Contexto:
Haz de circunferencias
Haz de circunferencias, son todas las circunferencias que comparten un mismo eje radical.
Para que esto ocurra todas tendrán sus centros sobre la misma recta diametral y que pasen por los dos mismos puntos del eje radical.
Al eje radical común se le llama base del haz.
Gracias de antemano.
Proposed translations
(English)
Change log
May 7, 2024 15:42: philgoddard changed "Field" from "Tech/Engineering" to "Other" , "Field (write-in)" from "Geometría métrica y descriptiva" to "(none)"
Proposed translations
+3
1 hr
Selected
pencil of circles
My daughter is a mechanical engineer and secondary school maths teacher. She's just shown me examples in Spanish and we've found this translation.
Pencil of circles
The Apollonian circles, two orthogonal pencils of circles
Any two circles in the plane have a common radical axis, which is the line consisting of all the points that have the same power with respect to the two circles. A pencil of circles (or coaxial system) is the set of all circles in the plane with the same radical axis. To be inclusive, concentric circles are said to have the line at infinity as a radical axis.
https://en.wikipedia.org/wiki/Pencil_(geometry)
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Note added at 2 hrs (2024-05-07 16:56:48 GMT)
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On the same Wikipedia page there's a reference for haz de circunferencias
La circunferencia de Apolonio es un famoso problema acerca de lugares geométricos: dados dos puntos A y B, se trata de determinar el lugar geométrico de los puntos del plano P que cumplen: PA/PB = r, siendo r una constante.
I clicked on the link and then clicked on the English version and found:
In geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa. These circles form the basis for bipolar coordinates. They were discovered by Apollonius of Perga, a renowned Greek geometer.
https://en.wikipedia.org/wiki/Apollonian_circles
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Note added at 2 hrs (2024-05-07 17:03:42 GMT)
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A pencil of circles is another name for specific families of circles who all share certain characteristics within the family.
An elliptical pencil of circles is the family of all circles that go through two given points. This is why another name for them is a two-point pencil. These circles are all intersecting, but never anywhere but these two points.
A hyperbolic pencil of circles, also called Apollonian circles, is the family of all circles that are orthogonal to the set of circles that go through 2 given points. Thus, the elliptical pencil of circles always has a corresponding hyperbolic pencil of circles that are orthogonal to every circle. None of the circles in the hyperbolic pencil intersect with each other, thus they are also called the zero-point pencil.
The third kind of pencil is the parabolic pencil. This is the family of circles which all have one common point, and thus are all tangent to each other, either internally or externally. Also, the orthogonal set of circles to a parabolic pencil is another parabolic pencil.
https://sites.math.washington.edu//~king/coursedir/m445w04/a...
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Note added at 2 hrs (2024-05-07 17:12:19 GMT)
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A family of circles that satisfy #2 and #6 is said to form a pencil of circles. The circles are said to be coaxal (sometimes coaxial), because all of them have the same axis of symmetry and any pair has the same radical axis. This property is obviously shared by a family of circles through a given point, say, A and tangent at A to each other. Perhaps, even more interestingly, the same holds for the family of circles that pass through two given points, A and B: their centers lie on the perpendicular bisector of AB; in addition, the radical axis of any pair passes through their common points: A and B. Since any pairs of circles that have the same radical axis are bound to have their centers collinear, sharing the radical axis by any pair of circles in the family is the defining property of the circles.
https://www.cut-the-knot.org/Curriculum/Geometry/CoaxalCircl...
Pencil of circles
The Apollonian circles, two orthogonal pencils of circles
Any two circles in the plane have a common radical axis, which is the line consisting of all the points that have the same power with respect to the two circles. A pencil of circles (or coaxial system) is the set of all circles in the plane with the same radical axis. To be inclusive, concentric circles are said to have the line at infinity as a radical axis.
https://en.wikipedia.org/wiki/Pencil_(geometry)
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Note added at 2 hrs (2024-05-07 16:56:48 GMT)
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On the same Wikipedia page there's a reference for haz de circunferencias
La circunferencia de Apolonio es un famoso problema acerca de lugares geométricos: dados dos puntos A y B, se trata de determinar el lugar geométrico de los puntos del plano P que cumplen: PA/PB = r, siendo r una constante.
I clicked on the link and then clicked on the English version and found:
In geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa. These circles form the basis for bipolar coordinates. They were discovered by Apollonius of Perga, a renowned Greek geometer.
https://en.wikipedia.org/wiki/Apollonian_circles
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Note added at 2 hrs (2024-05-07 17:03:42 GMT)
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A pencil of circles is another name for specific families of circles who all share certain characteristics within the family.
An elliptical pencil of circles is the family of all circles that go through two given points. This is why another name for them is a two-point pencil. These circles are all intersecting, but never anywhere but these two points.
A hyperbolic pencil of circles, also called Apollonian circles, is the family of all circles that are orthogonal to the set of circles that go through 2 given points. Thus, the elliptical pencil of circles always has a corresponding hyperbolic pencil of circles that are orthogonal to every circle. None of the circles in the hyperbolic pencil intersect with each other, thus they are also called the zero-point pencil.
The third kind of pencil is the parabolic pencil. This is the family of circles which all have one common point, and thus are all tangent to each other, either internally or externally. Also, the orthogonal set of circles to a parabolic pencil is another parabolic pencil.
https://sites.math.washington.edu//~king/coursedir/m445w04/a...
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Note added at 2 hrs (2024-05-07 17:12:19 GMT)
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A family of circles that satisfy #2 and #6 is said to form a pencil of circles. The circles are said to be coaxal (sometimes coaxial), because all of them have the same axis of symmetry and any pair has the same radical axis. This property is obviously shared by a family of circles through a given point, say, A and tangent at A to each other. Perhaps, even more interestingly, the same holds for the family of circles that pass through two given points, A and B: their centers lie on the perpendicular bisector of AB; in addition, the radical axis of any pair passes through their common points: A and B. Since any pairs of circles that have the same radical axis are bound to have their centers collinear, sharing the radical axis by any pair of circles in the family is the defining property of the circles.
https://www.cut-the-knot.org/Curriculum/Geometry/CoaxalCircl...
Note from asker:
Thanks, Helena, it might work! |
Peer comment(s):
agree |
philgoddard
: So 'family' would be OK as well. // You're right, it's a particular type of family.
18 mins
|
Hmm, not sure about that. I would use 'pencils of circles' but only because I'm not an expert on the matter. Half an hour ago, I would have said that a pencil is an instrument used for writing and drawing!
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agree |
neilmac
: Interesting new use of "pencil".. :-)
2 hrs
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Hi, Neil. You learn something new every day.
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neutral |
Francois Boye
: Although the definition of a pencil is rather vague, the common characteristic is that the pencil is completely determined by any two of its members. Analogously, a set of geometric objects that are determined by any three of its members is called a bundl
4 hrs
|
Thank you for your opinion, Francois. I'm sure the Asker would appreciate further information to help her decide the right answer.
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agree |
liz askew
23 hrs
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Hi, Liz! Thanks for confirming I'm right :-)
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4 KudoZ points awarded for this answer.
Comment: "Selected automatically based on peer agreement."
+1
2 hrs
families of circles
Note from asker:
Thanks! |
6 hrs
Circle bundles
http://users.math.uoc.gr/~pamfilos/eGallery/problems/CircleB...
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Note added at 9 hrs (2024-05-08 00:47:58 GMT)
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https://www.google.com/search?q=circle bundles&sca_esv=fa48f...
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Note added at 9 hrs (2024-05-08 00:47:58 GMT)
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https://www.google.com/search?q=circle bundles&sca_esv=fa48f...
Note from asker:
Thanks for your proposal |
Peer comment(s):
neutral |
philgoddard
: Your first reference is a mediocre translation from Greek, and your second from a completely different area of mathematics.
39 mins
|
No! This is a math concept used in topology. Did you read the links? Nothing is médiocre here.. No Greek word was used!//Which areas of maths are you talking about?
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1 day 50 mins
circumference beams
In geometrical mathematics a circumference is the boundary of a specific geometric figure, particularly a circle, or it's the length of a closed geometric curve. (thefreedictionary.com)
"The radical axis of 2 non-concentric circles is the set of points whose power with respect to the circles is equal."
https://en.wikipedia.org/wiki/Radical_axis
"A beam is a structural element which resists loads primarily. It's applied laterally across the axis of a beam.
Traditionally beams are descriptions of building or civil engineering structural elements where the beams are horizontal and carry or support vertical loads."
https://en.wikipedia.org/wiki/Beam_(structure)
"The radical axis of 2 non-concentric circles is the set of points whose power with respect to the circles is equal."
https://en.wikipedia.org/wiki/Radical_axis
"A beam is a structural element which resists loads primarily. It's applied laterally across the axis of a beam.
Traditionally beams are descriptions of building or civil engineering structural elements where the beams are horizontal and carry or support vertical loads."
https://en.wikipedia.org/wiki/Beam_(structure)
1 day 21 hrs
coaxial circles // coaxial system of circles // pencil of coaxial circles
Efectivamente, el original se refiere al conjunto de círculos que comparte un mismo eje radical.
Some refs:
Coaxial circles
https://dlmf.nist.gov/search/search?q=coaxial circles
Coaxial system of circles
https://www.toppr.com/ask/question/a-system-of-circles-is-sa...
Two orthogonal pencils of coaxial circles. Dashed circles are centered on the y axis and go through the points −1 and 1. Dotted circles are centered on the x axis and intersect dashed circles at the right angle.
https://www.researchgate.net/figure/Two-orthogonal-pencils-o...
Circles (F2AA'), (F2BB'), (F2CC') are coaxial
https://artofproblemsolving.com/community/c2735h1454926_ferm...
If a set of circles have the same radical axes, then we say they are coaxial. A collection of such circles is called a pencil of coaxial circles.
https://www.google.com/url?sa=t&source=web&rct=j&opi=8997844...
Some refs:
Coaxial circles
https://dlmf.nist.gov/search/search?q=coaxial circles
Coaxial system of circles
https://www.toppr.com/ask/question/a-system-of-circles-is-sa...
Two orthogonal pencils of coaxial circles. Dashed circles are centered on the y axis and go through the points −1 and 1. Dotted circles are centered on the x axis and intersect dashed circles at the right angle.
https://www.researchgate.net/figure/Two-orthogonal-pencils-o...
Circles (F2AA'), (F2BB'), (F2CC') are coaxial
https://artofproblemsolving.com/community/c2735h1454926_ferm...
If a set of circles have the same radical axes, then we say they are coaxial. A collection of such circles is called a pencil of coaxial circles.
https://www.google.com/url?sa=t&source=web&rct=j&opi=8997844...
Discussion
As for set... I am not very sure... but it is an option. Thanks!
http://piziadas.com/en/2013/05/geometria-metrica-haces-de-ci...
http://en.wikipedia.org/wiki/Radical_axis